Find the measure of the arc or central angle indicated. Assume that the lines which’s appear to be diameters are actual diameters.

m∠HKF = 87°

Solution:

Given data:

m(ar JF) = 135° and m(ar GH) = 42°

GJ is the diameter of the circle.

Angle in a diameter is 180°.

⇒ m(ar JF) + m(ar FG) = 180°

⇒ 135° + m(ar FG) = 180°

Subtract 135° from both sides of the equation.

⇒ m(ar FG) = 45°

⇒ m(ar FGH) = m(ar FG) + m(ar GH)

⇒ m(ar FGH)= 45° + 42°

⇒ m(ar FGH) = 87°

The measure of the central angle is congruent to the measure of the intercepted arc.

⇒ m∠HKF = m(ar FGH)

⇒ m∠HKF = 87°

10000000000000000000000000000000

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°